具有疾病复发的SVIR反应扩散传染病模型的动力学分析
首发时间:2022-04-11
摘要:基于部分感染者康复后变回易感者将再次被感染以及人群的移动对疾病传播的影响,本文主要研究带疫苗接种项且具非线性发生率的SVIR反应扩散传染病模型。论文首先验证了解的存在唯一性以及正性,进而得到基本再生数$\mathcal{R}_0$。进一步获知:$\mathcal{R}_0<1$ 时,无病平衡态$E_0$全局吸引;$\mathcal{R}_0>1$ 时,疾病是一致持久的。
关键词: 应用数学 反应扩散方程 SVIR传染病模型 基本再生数 无病平衡态 一致持久
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Dynamics of a reaction-diffusion SVIR model with disease relapse
Abstract:Based on the fact that some infected may be re-infected after recovery and the movement of population may affect the spread of epidemics, this paper mainly studied the model of SVIR reaction-diffusion infectious with vaccination items and nonlinear incidence. Firstly, we prove the existence, uniqueness and positivity of the solution, and furthermore we get the basic reproduction number $\mathcal{R}_0$. We further get that the disease-free stable state $E_0$ is globally attractive when $\mathcal{R}_0<1$ and the epidemic is uniform persistence when $\mathcal{R}_0>1$.
Keywords: Applied mathematics Reaction-diffusion equation SVIR epidemic model Basic reproduction number Disease-free stable state Uniform persistence
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具有疾病复发的SVIR反应扩散传染病模型的动力学分析
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